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anonymous

  • one year ago

5th root (-3)^5 ._.

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  1. kropot72
    • one year ago
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    It can be written as the power of a power: \[\large \sqrt[5]{(-3)^{5}}=((-3)^{5})^\frac{1}{5}\]

  2. kropot72
    • one year ago
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    Just multiply the indices (5 * (1/5).

  3. misty1212
    • one year ago
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    HI!!

  4. misty1212
    • one year ago
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    the fifth root of whatever to the power of five is whatever

  5. misty1212
    • one year ago
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    \[\huge \sqrt[5]{\diamondsuit^5}=\diamondsuit\]

  6. anonymous
    • one year ago
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    So if it's the same number it's going to be whatever the inside number is? (I have no clue if that made sense)

  7. anonymous
    • one year ago
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    @misty1212 Do you think you could help me with another problem?

  8. misty1212
    • one year ago
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    sure

  9. misty1212
    • one year ago
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    and yes, it is the same number that is inside, so your answer should be \(-3\)

  10. anonymous
    • one year ago
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    Cool, um, my next question is a 5th root of -1/32

  11. anonymous
    • one year ago
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    I don't understand fractions all that well and since I'm new to this whole 5th root, I'm extremely confused about it.

  12. misty1212
    • one year ago
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    your job is to think of a number that, when raised to the fifth power, is 32

  13. misty1212
    • one year ago
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    don't think too hard , it is easy to come by that is not the final answer btw, but that is the first step

  14. misty1212
    • one year ago
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    if you do not get it, let me know if you do, say it

  15. anonymous
    • one year ago
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    So it'd just be multiplying something by itself to get to 32?

  16. misty1212
    • one year ago
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    yes one number, multiplied by itself five times, to give 32

  17. misty1212
    • one year ago
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    i will be happy to tell you if you like

  18. anonymous
    • one year ago
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    Would it be 2? and since it's a negative 32, the answer would be -2?

  19. misty1212
    • one year ago
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    yes \(2^5=32\) so \(\sqrt[5]{32}=2\) but as i said, we are still not done

  20. misty1212
    • one year ago
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    you want \[\sqrt{-\frac{1}{32}}\] which is the same as \[\frac{\sqrt[5] 1}{\sqrt[5]{-32}}\]

  21. misty1212
    • one year ago
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    \[\sqrt[5]{1}=1\] and \[\sqrt[5]{-32}=-2\]

  22. anonymous
    • one year ago
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    So would it be the 5th root 1 over -2?

  23. misty1212
    • one year ago
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    no it would just be \[-\frac{1}{2}\]

  24. misty1212
    • one year ago
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    not the fifth root, you already took the fifth root

  25. anonymous
    • one year ago
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    Ohhh, I see now.

  26. misty1212
    • one year ago
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    ok good !!

  27. anonymous
    • one year ago
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    Thank you! :)

  28. misty1212
    • one year ago
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    \[\huge \color\magenta\heartsuit\]

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